But sloth, he does not know the acceleration, cause he does not know the initial velocity. I am not understanding how your equation gives this? Your building pressure in a barrel, and accelerating, and keep accelerating until your bullet leaves the barrel, then start decellerating.

His problem is not linear and has many varibles other than length. Like powder capacity, powder type, and I believe the bullet used, rifling (resistence or lack of to build pressure), etc.

From what i have seen, 25 to 30fps per an inch from 18" to 26", after or before that, it starts dropping off do to powder and pressure capacity of the caliber. Kinda like having a 50gal compressor vs. a 10 gal.

There was a good article in rifle mag that showed 44 mag tests cutting off the barrel and measuring velocity. What it showed is velocity loss was significant at when above 4", but below that it leveled off. I will try to find it.